Graph edit distance or graph edit pseudo-distance?

Graph Edit Distance has been intensively used since its appearance in 1983. This distance is very appropriate if we want to compare a pair of attributed graphs from any domain and obtain not only a distance, but also the best correspondence between nodes of the involved graphs. In this paper, we want to analyse if the Graph Edit Distance can be really considered a distance or a pseudo-distance, since some restrictions of the distance function are not fulfilled. Distinguishing between both cases is important because the use of a distance is a restriction in some methods to return exact instead of approximate results. This occurs, for instance, in some graph retrieval techniques. Experimental validation shows that in most of the cases, it is not appropriate to denominate the Graph Edit Distance as a distance, but a pseudo-distance instead, since the triangle inequality is not fulfilled. Therefore, in these cases, the graph retrieval techniques not always return the optimal graph

Correspondence consensus of two sets of correspondences through optimisation functions.

We present a consensus method which, given the two correspondences between sets of elements generated by separate entities, enounces a final correspondence consensus considering the existence of outliers. Our method is based on an optimisation technique that minimises the cost of the correspondence while forcing (to the most) to be the mean correspondence of the two original correspondences. The method decides the mapping of the elements that the original correspondences disagree and returns the same element mapping when both correspondences agree. We first show the validity of the method through an experiment in ideal conditions based on palmprint identification, and subsequently present two practical experiments based on image retrieval